Gravitational Relativity Paradox.

A well known consequence of Einstein's Special Relativity theory is that time "slows" down on a moving object (AKA reference frame) by a factor of gamma:

(1 - V2/ C2)  1

Where V is the object's velocity and C is the speed of light.

Now, I ask you to imagine a cylinder about the size and density of the earth and a light year in length. Please suspend your engineering credulity enough that you can think of such an unbuildable object for the duration of this gedankenexperiment. Also, we'll assume that there is no atmosphere around this unlikely cylinder, so realities such as air resistance will play no part in the upcoming discussion.

On this cylinder, about a light month from the end (so as to avoid any end effect non linearities of the gravitational field about the cylinder), is built a linear mass accelerator capable of accelerating small objects to 0.87 C. The axis of this accelerator and that of the unbuildable cylinder are parallel to each other.

You're all familiar with the high school physics experiment where a gun, with it's barrel exactly parallel to the ground, is fired. At the same time the gun is fired, a bullet is dropped. The fired and dropped bullet hit the ground at the same time. This is straightforward Newtonian physics, although it's usually enough to amaze those who've never seen it before.

Consider the same experiment done on our hypothetical cylinder. At the instant the bullet leaves the mass accelerator, a similar bullet is dropped from the same height as the muzzle of the accelerator. Each bullet has a clock which is started at the instant the bullet leaves the muzzle.

Both bullets fall at the same speed, as they are both subject to the same gravitational field (Now you see the need for such a long cylinder, a bullet traveling at 0.87 C would shoot off the surface of the earth with hardly any deflection.). When the dropped bullet hits the ground, it's clock will read, say 1 second. When the accelerated bullet hits the ground at the same time, it's clocks will read 0.5 seconds, because of the time dilation given in the above equation.

Nothing strange about this, unless you were to ask an observer (who can ride a bullet at 0.87 C? My bogosity meter is pegged!) to measure the gravitational field that caused the bullet to fall. He/She will conclude that the field is a function of the velocity:

V = to(gamma))2

Here to is the time as measured in the reference frame that is at rest.

Conversely, it is also possible that the accelerated bullet falls so that It's clock registers 1 second when it hits the ground. Then the observer at rest will conclude that the gravitational field is also a function of velocity:

V = to(gamma))½

I have no idea which of these effects is observed. Is it accounted for by general relativity? If you think you have an answer, I'd like to hear from you:

Drop me a line.

1) For more about special relativity, and relativity in general, have a look at the
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